Quasi-linear elliptic equations with data in $L^{1}$ on Riemannian manifold

Abdellah Abnoune; El Houssine Azroul; Academic Editor: Youssef EL FOUTAYENI

Research Communication | Open Access
Volume 2019 | Communication ID 238

Quasi-linear elliptic equations with data in $L^{1}$ on Riemannian manifold

Abdellah Abnoune, El Houssine Azroul

Academic Editor: Youssef EL FOUTAYENI

Received	Accepted	Published
Jan 31, 2019	Feb 26, 2019	Mar 01, 2019

Abstract: This work is dedicated to the study of quasi-linear elliptic problems with $L^1$ data, the simple model will be the next equation on $ (M,g) $ a Riemannian manifold $$-\Delta_{p} u=f$$ Where $f\in L^{1}(M) $ .Our goal is to develop the functional framework and tools that are necessary to prove the existence and the uniqueness of the solution for the previous problem. Notice that our argument can be used to deal with a more general class of quasi-linear equations.